One of Stacy's early television roles was in 1958 on the syndicated romantic comedy, How to Marry a Millionaire, with Barbara Eden and Merry Anders. He portrayed a federal police agency officer fighting crime in the Caribbean in the 1975 TV series Caribe. He played Barabbas in the 1977 Jesus of Nazareth (miniseries), and portrayed Jonas Steele, a psychic and Scout of the United States Army in the 1982 CBS miniseries, The Blue and the Gray. He later portrayed Mike Hammer in the CBS television series Mickey Spillane's Mike Hammer and The New Mike Hammer from 1984 to 1987. He returned to the role of Hammer in Mike Hammer, Private Eye, a new syndicated series that aired from 1997 to 1998.
In 2000, he played the cantankerous father Ken Titus in the title family of Fox's sitcom Titus. Cast members of Titus have commented they enjoyed working with Stacy because, even with the dryest line the writers could invent, Stacy would find a way to make the line funny.
Fans of The Simpsons may also recognize Stacy's voice in the recurring role of Duff Brewery President, Howard K. Duff VIII, beginning with the 12th season episode, "Hungry, Hungry Homer", wherein Homer attempts to stop Howard K. Duff from moving the Springfield Isotopes baseball team to Albuquerque by staging a hunger strike.
Stacy guest starred in the sitcom Will & Grace. He also had a recurring role as Warden Henry Pope in the Fox drama Prison Break.